U.S. patent number 8,502,962 [Application Number 12/945,775] was granted by the patent office on 2013-08-06 for computer readable storage medium including effective light source calculation program, and exposure method.
This patent grant is currently assigned to Canon Kabushiki Kaisha. The grantee listed for this patent is Hironobu Fujishima, Miyoko Kawashima, Kenji Yamazoe. Invention is credited to Hironobu Fujishima, Miyoko Kawashima, Kenji Yamazoe.
United States Patent |
8,502,962 |
Kawashima , et al. |
August 6, 2013 |
Computer readable storage medium including effective light source
calculation program, and exposure method
Abstract
A storage medium includes a program which causes a computer to
execute a method of calculating a light intensity distribution on a
pupil plane of an illumination optical system. The method includes:
determining an impulse response function of a projection optical
system by performing Fourier transform on a pupil function of the
projection optical system; setting a length to a second zero point
of the impulse response function as a response length, extracting,
from elements forming a target pattern, only elements inside am
area within radius which is response length, and determining a
function indicating the extracted pattern as an image function; and
obtaining the light intensity distribution based on the pupil
function, the determined impulse response function, and the
determined image function.
Inventors: |
Kawashima; Miyoko (Haga-gun,
JP), Yamazoe; Kenji (Utsunomiya, JP),
Fujishima; Hironobu (Utsunomiya, JP) |
Applicant: |
Name |
City |
State |
Country |
Type |
Kawashima; Miyoko
Yamazoe; Kenji
Fujishima; Hironobu |
Haga-gun
Utsunomiya
Utsunomiya |
N/A
N/A
N/A |
JP
JP
JP |
|
|
Assignee: |
Canon Kabushiki Kaisha
(JP)
|
Family
ID: |
44061864 |
Appl.
No.: |
12/945,775 |
Filed: |
November 12, 2010 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20110122394 A1 |
May 26, 2011 |
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Foreign Application Priority Data
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Nov 20, 2009 [JP] |
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2009-265530 |
Oct 26, 2010 [JP] |
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2010-240106 |
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Current U.S.
Class: |
355/77; 355/71;
355/67 |
Current CPC
Class: |
G03F
7/705 (20130101); G03F 7/70508 (20130101); G03F
7/70091 (20130101); G03F 7/70083 (20130101) |
Current International
Class: |
G03B
27/32 (20060101); G03B 27/54 (20060101); G03B
27/72 (20060101) |
Field of
Search: |
;355/53,67,71,77
;716/51,53 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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6-120119 |
|
Apr 1994 |
|
JP |
|
2002-334836 |
|
Nov 2002 |
|
JP |
|
2004-128108 |
|
Apr 2004 |
|
JP |
|
2008-040470 |
|
Feb 2008 |
|
JP |
|
Other References
"Interference and diffraction with partially coherent light,"
Principles of Optics, Cambridge University Press, 1999, 7th
(extended) edition, pp. 554-632. Cited in spec. Previously
submitted Nov. 12, 2010. cited by applicant.
|
Primary Examiner: Gordon; Steven H Whitesell
Attorney, Agent or Firm: Rossi, Kimms & McDowell LLP
Claims
What is claimed is:
1. A non-transitory computer readable storage medium storing a
program executable by a computer to execute a method of calculating
a light intensity distribution to be formed on a pupil plane of an
illumination optical system in an exposure apparatus which
illuminates an original with light emitted from said illumination
optical system, and exposes a substrate by projecting a pattern of
the illuminated original onto the substrate via a projection
optical system, the method comprising the steps of: determining an
impulse response function of said projection optical system through
a process of performing Fourier transform on a pupil function of
said projection optical system; setting a length to a second zero
point of the impulse response function from the origin as a
response length, extracting, from elements forming a target pattern
to be formed on the substrate, only elements for each of which the
spacing to an adjacent element is equal to or smaller than the
response length, and determining a function indicating the
extracted pattern as an image function; and obtaining the light
intensity distribution to be formed on the pupil plane of said
illumination optical system based on the pupil function, the
determined impulse response function, and the determined image
function.
2. The non-transitory computer readable storage medium according to
claim 1, wherein the pupil function includes an aberration of said
projection optical system.
3. The non-transitory computer readable storage medium according to
claim 1, wherein the step of obtaining the light intensity
distribution comprises the steps of: executing a division process
of dividing the determined image function by the impulse response
function, and performing inverse Fourier transform on the function
having performed the division process; and obtaining the light
intensity distribution to be formed on the pupil plane of the
illumination optical system by performing a division process of
dividing the function having performed inverse Fourier transform by
a complex conjugate function of the pupil function.
4. The non-transitory computer readable storage medium according to
claim 1, wherein letting .lamda. be a wavelength of the light which
illuminates the original, and NA be a numerical aperture of said
projection optical system, the step of determining the impulse
response function comprises, after performing Fourier transform on
the pupil function, the step of replacing coordinates on an image
plane of said projection optical system with coordinates on the
pupil plane of said projection optical system by dividing the
coordinates on the image plane by (NA/.lamda.), and replacing a
nonzero value at a point at which an impulse response function is
zero.
5. A non-transitory computer readable storage medium storing a
program executable by a computer to execute a method of calculating
a light intensity distribution to be formed on a pupil plane of an
illumination optical system in an exposure apparatus which
illuminates an original with light emitted from said illumination
optical system, and exposes a substrate by projecting a pattern of
the illuminated original onto the substrate via a projection
optical system, the method comprising the steps of: determining an
impulse response function of said projection optical system through
a process of performing Fourier transform on a pupil function of
said projection optical system; setting a length to a second zero
point of the impulse response function from the origin as a
response length, extracting a pattern from elements forming a
target pattern to be formed on the substrate, and determining a
function indicating the extracted pattern as an image function; and
obtaining the light intensity distribution to be formed on the
pupil plane of said illumination optical system based on the pupil
function, the determined impulse response function, and the
determined image function, wherein the step of determining the
image function comprises the steps of: calculating a diffracted
light distribution of the target pattern to be formed on the
substrate; extracting diffracted light components having the same
phase from the calculated diffracted light distribution; performing
Fourier transform on the extracted diffracted light components;
obtaining a function of peak positions of the diffracted light
components having performed Fourier transform, within a range
enclosed with a circle centering around an optical axis of said
projection optical system and having a diameter not more than the
response length; and convolving a function representing a shape of
an element forming the target pattern into the obtained function of
peak positions, and determining the convolved function as an image
function.
6. A non-transitory computer readable storage medium storing a
program executable by a computer to execute a method of calculating
a light intensity distribution to be formed on a pupil plane of an
illumination optical system in an exposure apparatus which
illuminates an original with light emitted from said illumination
optical system, and exposes a substrate by projecting a pattern of
the illuminated original onto the substrate via a projection
optical system, the method comprising the steps of: determining an
impulse response function of said projection optical system through
a process of performing Fourier transform on a pupil function of
said projection optical system; setting a length to a second zero
point of the impulse response function from the origin as a
response length, extracting a pattern from elements forming a
target pattern to be formed on the substrate, and determining a
function indicating the extracted pattern as an image function; and
obtaining the light intensity distribution to be formed on the
pupil plane of said illumination optical system based on the pupil
function, the determined impulse response function, and the
determined image function, wherein letting I(x,y) be an image of
the target pattern to be formed on the substrate, a(f,g) be a
diffracted light distribution of the target pattern at a point
(f,g) on the pupil plane of said projection optical system, F be
Fourier transform, and F.sup.-1 be inverse Fourier transform, the
step of determining the image function comprises the step of
calculating an image function r(x,y) by substituting the image
I(x,y) of the target pattern and the diffracted light distribution
a(f,g) of the target pattern into a right side of
.function..function..function..times..function..function..function..funct-
ion. ##EQU00005## and replacing with zero a value of the image
function for which a distance from an optical axis of said
projection optical system is larger than the response length.
7. A method of calculating a light intensity distribution to be
formed on a pupil plane of an illumination optical system in an
exposure apparatus which illuminates an original with light emitted
from the illumination optical system and exposes a substrate by
projecting a pattern of the illuminated original onto the substrate
via a projection optical system, the method, which is executable by
a computer, comprising the steps of: determining an impulse
response function of the projection optical system through a
process of performing Fourier transform on a pupil function of the
projection optical system; setting a length from the origin to a
second zero point of the impulse response function as a response
length, extracting, from elements forming a target pattern to be
formed on the substrate, only elements for each of which the
spacing to an adjacent element is equal to or smaller than the
response length, and determining a function indicating the
extracted pattern as an image function; and obtaining the light
intensity distribution to be formed on the pupil plane of the
illumination optical system based on the pupil function, the
determined impulse response function, and the determined image
function.
8. The method according to claim 7, wherein the pupil function
includes an aberration of the projection optical system.
9. The method according to claim 7, further comprising the steps
of: executing a division process of dividing the determined image
function by the impulse response function, and performing inverse
Fourier transform on the function having performed the division
process; and obtaining the light intensity distribution to be
formed on the pupil plane of the illumination optical system by
performing a division process of dividing the function having
performed inverse Fourier transform by a complex conjugate function
of the pupil function.
10. A method of calculating a light intensity distribution to be
formed on a pupil plane of an illumination optical system in an
exposure apparatus which illuminates an original with light emitted
from the illumination optical system and exposes a substrate by
projecting a pattern of the illuminated original onto the substrate
via a projection optical system, the method, which is executable by
a computer, comprising the steps of: determining an impulse
response function of the projection optical system through a
process of performing Fourier transform on a pupil function of the
projection optical system; setting a length from the origin to a
second zero point of the impulse response function as a response
length, extracting a pattern from elements forming a target pattern
to be formed on the substrate, and determining a function
indicating the extracted pattern as an image function; and
obtaining the light intensity distribution to be formed on the
pupil plane of the illumination optical system based on the pupil
function, the determined impulse response function, and the
determined image function, wherein the step of determining the
image function comprises the steps of: calculating a diffracted
light distribution of the target pattern to be formed on the
substrate; extracting diffracted light components having the same
phase from the calculated diffracted light distribution; performing
Fourier transform on the extracted diffracted light components;
obtaining a function of peak positions within a area of not more
than the response length; and convolving a function representing a
shape of an element forming the target pattern into the obtained
peak position function, and determining the convolved function as
an image function.
11. A method of calculating a light intensity distribution to be
formed on a pupil plane of an illumination optical system in an
exposure apparatus which illuminates an original with light emitted
from the illumination optical system and exposes a substrate by
projecting a pattern of the illuminated original onto the substrate
via a projection optical system, the method, which is executable by
a computer, comprising the steps of: determining an impulse
response function of the projection optical system through a
process of performing Fourier transform on a pupil function of the
projection optical system; setting a length from the origin to a
second zero point of the impulse response function as a response
length, extracting a pattern from elements forming a target pattern
to be formed on the substrate, and determining a function
indicating the extracted pattern as an image function; and
obtaining the light intensity distribution to be formed on the
pupil plane of the illumination optical system based on the pupil
function, the determined impulse response function, and the
determined image function, wherein letting r(x,y) be the image
function, I(x,y) be an image of the target pattern to be formed on
the substrate, a(f,g) be a diffracted light distribution of the
target pattern at a point (f,g) on the pupil plane of the
projection optical system, F be Fourier transform, and F.sup.-1 be
inverse Fourier transform, the step of determining the image
function comprises the step of calculating the image function
r(x,y) by substituting the image I(x,y) of the target pattern and
the diffracted light distribution a(f,g) of the target pattern into
a right side of
.function..function..function..times..function..function..function..funct-
ion. ##EQU00006## and replacing with zero a value of the image
function for which a distance from an optical axis of the
projection optical system is larger than the response length.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a computer readable storage medium
including an effective light source calculation program, and an
exposure method.
2. Description of the Related Art
An exposure apparatus has conventionally been used when
manufacturing fine semiconductor devices such as semiconductor
memories and logical circuits by using the photolithography
technique. The exposure apparatus projects a pattern (circuit
pattern) drawn on a mask (reticle) as an original onto a substrate
such as a wafer by using a projection optical system, thereby
transferring the pattern onto the substrate. Recently, the
micropatterning techniques for semiconductor devices have advanced,
and the exposure apparatus is required to form patterns having
dimensions smaller than the exposure wavelength (the wavelength of
exposure light). In the formation of fine patterns like these, the
image quality is affected by the illumination condition (effective
light source) used to illuminate the mask. This makes it important
to set an optimum effective light source.
Accordingly, a trial and error method is generally used where the
best effective light source is selected among a plurality of
possible ones by evaluating each corresponding optical images
(aerial images). However, this method requires time and labor.
Therefore, a deterministic method of the effective light source is
desirable. Generally, the determination of an effective light
source requires the calculation of many optical images. For
example, an effective light source is two-dimensionally divided
into a plurality of elements, and these elements are regarded as
point light sources. Then, an optical image attributed to each
point light source is calculated, and the point light sources
contributing to faithful realization of the original pattern are
adapted. In this way, an effective light source can be optimized.
The optimization scheme of an effective light source like this is
disclosed in Japanese Patent Laid-Open Nos. 6-120119, 2002-334836,
and 2004-128108. However, since this method must calculate many
optical images (aerial images), it takes an enormous time to
determine the effective light source.
SUMMARY OF THE INVENTION
The present invention calculates an effective light source within a
short time without performing any time-consuming calculation of
image formation. Furthermore, the present invention calculates an
effective light source so as to reduce a decrease in image
formation performance in a case including an aberration as compared
with a case including no aberration.
According to one aspect of the present invention, there is provided
a computer readable storage medium comprising a program which
causes a computer to execute a method of calculating a light
intensity distribution to be formed on a pupil plane of an
illumination optical system in an exposure apparatus which
illuminates an original with light emitted from the illumination
optical system, and exposes a substrate by projecting a pattern of
the illuminated original onto the substrate via a projection
optical system, the method comprising steps of: determining an
impulse response function of the projection optical system through
a process of performing Fourier transform on a pupil function of
the projection optical system; setting a length to a second zero
point of the impulse response function from the origin as a
response length, extracting, from elements forming a target pattern
to be formed on the substrate, only elements inside an area within
radius which is response length, and determining a function
indicating the extracted pattern as an image function; and
obtaining the light intensity distribution to be formed on the
pupil plane of the illumination optical system based on the pupil
function, the determined impulse response function, and the
determined image function.
Further features of the present invention will become apparent from
the following description of exemplary embodiments with reference
to the attached drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1A and 1B are flowcharts of a method of determining an
effective light source;
FIGS. 2A to 2E are exemplary views showing a target pattern, image
function, impulse response, and determined effective light
source;
FIGS. 3A to 3F are views showing a target pattern, image function,
and determined effective light source according to the first
embodiment;
FIGS. 4A and 4B are views showing a mask pattern and the
two-dimensional image of an aerial image obtained by using the
effective light source according to the first embodiment;
FIGS. 5A to 5F are views showing a target pattern, a diffracted
light distribution from the target pattern, pitch sampling, the
distribution of a function representing the shape, an image
function, and a determined effective light source according to the
second embodiment;
FIGS. 6A to 6E are views showing an illumination light source, a
mask pattern, and a two-dimensional image obtained by using the
mask pattern according to the second embodiment;
FIGS. 7A to 7E are views showing a target pattern, a determined
effective light source, and the two-dimensional image of an aerial
image obtained by using the effective light source;
FIG. 8 is a view showing an exposure apparatus;
FIGS. 9A to 9E are exemplary views showing a target pattern, an
effective light source distribution, and a mask pattern obtained
from the determined effective light source according to the fourth
embodiment; and
FIG. 10 is a view showing the CD focus characteristics of an aerial
image according to the fourth embodiment.
DESCRIPTION OF THE EMBODIMENTS
The present invention is applicable when manufacturing various
kinds of devices, for example, semiconductor chips such as an IC
and LSI, display devices such as a liquid crystal panel, detection
devices such as a magnetic head, and image sensing devices such as
a CCD, and generating original data (a mask pattern) for use in
micromechanics. Micromechanics herein mentioned is the technique of
forming a micron-order machine system having an advanced function
by applying the semiconductor integrated circuit fabrication
techniques to the manufacture of microstructures, or the machine
system itself. The present invention is usable as, for example, a
method of determining an effective light source for illuminating
original data (a mask pattern) for use in an exposure apparatus
including a projection optical system having a large numerical
aperture (NA), or an immersion exposure apparatus in which the
space between a projection optical system and wafer is filled with
a liquid.
Embodiments of the present invention will be explained below with
reference to the accompanying drawings. Note that the same
reference numerals denote the same parts in these drawings, and a
repetitive explanation will be omitted. In an exposure apparatus,
according to the partial coherent imaging theory, an aerial image
on the wafer plane can be calculated. Partial coherent image
formation requires the information of an effective light source.
The coherence herein mentioned is the degree of interference
depending to the distance on the mask surface, and means a
so-called spatial coherence. Also, the effective light source is a
light intensity distribution formed on the pupil of a projection
optical system when there is no mask. That is, determining the
effective light source is to calculate the light intensity
distribution to be formed on the pupil plane of an illumination
optical system.
The coherency of the effective light source is incorporated in a
TCC (Transmission Cross Coefficient). The TCC is defined on the
pupil plane of a projection optical system, and represents an
overlapped area of the effective light source, a pupil function of
the projection optical system, and a complex conjugate of the pupil
function of the projection optical system. Letting (f,g) be
coordinates on the pupil plane of the projection optical system,
S(f,g) be a function expressing the effective light source, and
P(f,g) be the pupil function, the TCC can be represented by:
TCC(f',g',f'',g'')=.intg..intg.S(f,g)P(f+f',g+g')P*(f+f'',g+g'')dfdg
(1) where *'' represents the complex conjugate, and the integral
range is -.infin. to .infin..
The pupil function is a function representing the pupil plane of
the projection optical system, and has information such as the
shape, size, and aberration of the pupil. The aberration of the
projection optical system, the polarization of illumination light,
resist information, and the like can be incorporated in the pupil
function P(f,g). In this specification, therefore, a simple
description "pupil function" sometimes includes the polarization,
aberration, and resists information. As indicated by equation (1),
the TCC is originally a four-dimensional function. In this
specification, however, this four-dimensional function will simply
be abbreviated as TCC in some cases. A function l(x,y) representing
an aerial image can be given by using the TCC, quadruple integral
by equation (2) by using a function a(f,g) expressing the spectral
distribution (diffracted light distribution) of a mask pattern on
the pupil plane of the projection optical system. The diffracted
light distribution a(f,g) of the mask pattern is a function
F(m(x,y)) obtained by performing Fourier transform on a function
m(x,y) expressing the mask pattern. Note that in equation (2), *
represents the complex conjugate and the integral range is
-.infin.to .infin.. M. Born, E. Wolf, "Principles of Optics",
Cambridge University Press, 1999, 7th (extended) edition, p.
554-632 explains a detailed explanation of equation (2).
I(x,y)=.intg..intg..intg..intg.TCC(f',g',f'',g'')a(f',g)a*(f'',g'').times-
.exp{-i2.pi.[(f'-f'')x+(g'-g'')y]}df'dg'df''dg'' (2)
Equations (3) and (4) are obtained by representing equation (2),
that is, the function I(x,y) expressing an aerial image, by
discretized variables, and deforming the function. In equation (4),
F.sup.-1 represents inverse Fourier transform.
.times..function.''.times..times.''.function.''.function..function.''.tim-
es..function.I.pi..function.'.times.'.times..times..function.''.function.'-
'''.times..function.'''' ##EQU00001##
W.sub.f',g' (f'',g'') is defined by equation (5) with respect to
certain fixed coordinates (f',g').
W.sub.f',g'(f'',g'')=TCC(f',g',f'',g'') (5)
Since Fourier transform and inverse Fourier transform are sometimes
interchangeably used, the expression can be altered as follows.
In addition, Y.sub.f',g'(x,y) can be described by equation (6)
below by changing the sequence of addition.
Y.sub.f',g'(x,y)=a*(f',g')exp[i2.pi.(f'x+g'y)].times.F[W.sub.f',g'(f'',g'-
')a(f'',g'')] (6)
Y.sub.f'',g''(x, y) is called an approximate aerial image. When
(f',g')=(0,0), the pupil function of the projection optical system
and the effective light source overlap each other. Therefore,
W.sub.0,0(f'',g'') obviously has the largest effect among all
two-dimensional transmission cross coefficients.
The effective light source can be determined by using equations (5)
and (6). Assuming that the coordinates of the pupil plane (f'',g'')
is rewritten to (f,g), the pupil function is P(f,g), and the image
function is r(x,y) the effective light source S(f, g) can be
expressed by following formula 7 or 8. Since the phase of the pupil
function is taken into consideration, a case including an
aberration can be processed. S(f,g)=1/P(f,g).times.F.left
brkt-bot.r*(x,y)/F[P*(f,g)].right brkt-bot. (7)
S(f,g)=1/P*(f,g).times.F.sup.-1[r(x,y)/F[P(f,g)]] (8)
An image function r(x,y) representing an image on the image plane
of the projection optical system is defined as follows. Solving
equations (5) and (6) yields equation (9), so the image function
can be obtained mathematically as follows:
.times..function..function..function..times..function..function..function-
..function. ##EQU00002##
The image function r(x,y) represented by equation (9) uses the
approximate aerial image I(x,y) and the diffracted light
distribution a(f,g). F[p(f,g)] as the impulse response of the
projection optical system determines the range within which the
approximate aerial image has an effective value. Letting .lamda. be
the wavelength of light (light illuminating an original) passing
through the projection optical system and NA be the numerical
aperture of the projection optical system, the approximate aerial
image is effective inside the area. The length from the origin to
the second zero point of F[p(f,g)] is about (7.016 (/NA)/(2.pi.)),
that is about 1.12 (/NA). Accordingly, the effective range of the
image function r(x,y) is 1.12 (.lamda./NA) or less. Although this
length more or less changes if there is an aberration, this length
is regarded as the response length. The effective light source
S(f,g) is a light source for resolving the image function r(x,y).
That is, this method obtains a light source that resolves the
pattern inside a distance equal to or smaller than the response
length. Also, the effective light source must, of course, be larger
than 0.5 (.lamda./NA) as the range within which the optical system
can be resolved.
If a minimum structure can be resolved in the relative positional
relationship of a target pattern, the whole target pattern can be
resolved. When the target pattern is a periodic pattern, it is only
necessary to consider a minimum unit structure within the range
equal to or smaller than the response length. Even for a general
pattern including a plurality of periodicities, the image function
r(x,y) need only be considered by extracting a pattern near the
above-mentioned effective range.
In equation (9), the approximate aerial image I(x,y) cannot
accurately be obtained if no light source is determined. However,
the image function can also be obtained by assuming that the
approximate aerial image I(x,y) is equal to a target pattern itself
or a partial image of the target pattern. Furthermore, it is in
practice necessary to obtain the diffracted light distribution of a
mask pattern as the diffracted light distribution a(f,g). However,
the image function is obtained by assuming that the diffracted
light distribution a(f,g) is equal to the diffracted light
distribution of a target pattern. Practical methods of calculating
the image function will be explained below.
[First Calculation Method of Image Function]
In the first method, it is assumed that the image function r(x,y)
is a minimum unit of a target pattern in the relative positional
relationship of the whole target pattern. More specifically, only
elements for each of which the spacing to an adjacent element is
equal to or smaller than the response length are extracted from
elements forming the target pattern, and a function indicating the
extracted pattern is determined as the image function. When the
target pattern is a periodic pattern having only one periodicity,
the effective light source S(f,g) can be determined by using the
image function determined by this method, instead of the image
function r(x,y) of equation (9).
[Second Calculation Method of Image Function]
In the first method, it should be noted that the pattern spacing in
a target pattern is not always limited to one period in respect of
the pattern periodicity. This is so because the pattern spacing
includes an n-fold (n is a positive integer) period. Since the
pattern periodicity can be expressed by a frequency space, a
minimum periodic structure is found if the diffracted light
distribution is obtained. However, even when the diffracted light
distribution is converted into the periodicity on the image plane
by Fourier transform, the minimum periodic structure disappears
because the positive and negative diffracted light components
cancel each other. Therefore, diffracted light components having
the same phase are extracted, and Fourier transform is performed by
including up to a region of 2NA/.lamda., thereby obtaining the
periodicity so as not to cancel the minimum periodic structure on
the image plane. An aerial image of adjacent pattern elements
extracted within the above-mentioned range is defined as the image
function (x,y). The second method is obtained by extending the
first method to an arbitrary pattern.
The second calculation method of the image function will be
explained below with reference to FIG. 1B. Information to be input
to a computer for calculating the image function includes the whole
or a part of target pattern data, the wavelength .lamda. of the
exposure light, and the numeral aperture NA of the projection
optical system. The computer calculates the pattern periodicity
based on the input information. First, in process 11, the computer
calculates the diffracted light distribution of the target pattern.
Then, in process 12, the computer extracts frequency components
having the same phase within the range twice as large as the pupil
radius, and performs Fourier transform on the extracted frequency
components. In process 12, the computer extracts only frequency
components equal to or larger (or smaller) than a certain value, in
order to extract frequency components having the same phase. In
process 13, from the image having performed Fourier transform, the
computer obtains peak positions within the range enclosed with a
circle centering around the optical axis of the projection optical
system and having a diameter equal to or smaller than the response
length, that is, about 1.12.times.(.lamda./NA) (pitch sampling). In
process 14, the computer sets a function representing the shape of
elements forming the target pattern. The function representing the
shape can be a function representing the shape itself of an element
of the target pattern, and can also be a function obtained by
approximating the shape of an element of the target pattern by a
function such as the Gaussian distribution. It is also possible to
define the function representing the shape from an intensity
distribution obtained by the calculation of image formation by
using a light source, in which an element of the target pattern is
preset, and the wavelength and numerical aperture of the projection
optical system. In process 15, the computer convolves the function
set in process 14 and representing the shape of an element of the
target pattern, into each point of the peak position extracted in
process 13, and adds up all the peak position points, thereby
calculating the image function.
[Third Calculation Method of Image Function]
In the third method, a computer calculates the image function by
equation (9) by letting I(x,y) be the aerial image of a target
pattern and a(f,g) be the diffracted light distribution of the
target pattern, around the optical axis of the projection optical
system. More specifically, the computer calculates the image
function r(x,y) by substituting the image I(x,y) of the target
pattern and the diffracted light distribution a(f,g) of the target
pattern into the right side of
.function..function..function..times..function..function..function..funct-
ion. ##EQU00003## The image function r(x,y) has a value in only the
range enclosed with a circle centering around the optical axis of
the projection optical system and having a diameter equal to or
smaller than the response length, that is, about
1.12.times.(.lamda./NA), and is replaced by zero in a position
larger than the response length. In this case, there is instability
that these settings change the obtained effective light source.
However, the second and third image function calculation methods
are widely generalized methods for arbitrary patterns.
[Determination of Effective Light Source]
FIG. 1A is a schematic block diagram showing a method of
calculating a light intensity distribution to be formed on the
pupil plane of an illumination optical system, that is, a method of
determining the effective light source. A program causes a computer
to execute the method. The method of determining the effective
light source shown in FIG. 1A is based on equation (8). In process
1, the computer calculates the image function by using the first to
third methods described above. In process 2, the computer performs
Fourier transform on the pupil function of the projection optical
system. The function obtained by Fourier transform of the pupil
function is the impulse response (impulse response function) of the
projection optical system. The length to the second zero point of
the impulse response from the origin is obtained as the response
length. In process 2, the computer converts the coordinates on the
pupil plane into the coordinates on the image plane of the
projection optical system, it is multiplied by 1/(NA/.lamda.).
Also, in process 2, the computer replaces a nonzero finite value at
a point at which impulse response is a zero.
In process 3, the computer performs a division process to divide
the image function calculated in process 1 by the impulse response
calculated in process 2, and performs inverse Fourier transform on
the function having performed the division process. In process 4,
the computer performs a division process to divide the function
having performed inverse Fourier transform in process 3 by the
complex conjugate function of the pupil function, thereby obtaining
the effective light source. That is, in process 4, the computer
takes the real part of the distribution obtained by process 3, and
replaces all negative intensities with zeros. Note that a light
source distribution exceeding the ratio of the NAs of the
illumination optical system to the NA of the projection optical
system may be replaced with zero. Note also that the division
process need only perform a division as a result, and therefore,
includes performing a division process in an arithmetic circuit of
the computer, for example, a bit shift by the arithmetic circuit.
The same applies to the following explanation.
The explanation will be made by taking a pattern as shown in FIG.
2A as an example. Assume that the wavelength .lamda. of ArF for
illuminating an original is 193 nm, the NA of the projection
optical system is 1.35, the central distance (pitch) between
elements of a target pattern is 130 nm, and the dimension of one
side of each target pattern element is 65 nm. The response length
is about 160 nm. FIG. 2B shows the image function calculated by the
computer by extracting target pattern elements for which the
spacing between the central positions of the elements is 160 nm or
less, by using the first calculation method of the image function
in process 1. The impulse response of the projection optical system
calculated by the computer in process 2 is as shown in FIGS. 2C and
2D. FIG. 2C shows the two-dimensional intensity distribution of the
impulse response of the projection optical system. FIG. 2D shows
the one-dimensional section of FIG. 2C. In processes 3 and 4, the
computer obtains an effective light source as shown FIG. 2E. In
this case, the ratio of the NAs of the illumination optical system
to the NA of the projection optical system was 1. Thus, as a light
source suited to the target pattern as shown in FIG. 2A, the
effective light source distribution as shown in FIG. 2E, that is, a
quadrupole illumination distribution is obtained. This result
matches a well-known illumination distribution. It is also possible
to form mask pattern data from the light source thus obtained and
the target pattern. The mask pattern formation method is disclosed
in Japanese Patent Laid-Open No. 2008-040470.
Details of the above-mentioned processes will be explained below
with reference to the first to third embodiments. In all the first
to third embodiments, the NA of a projection optical system of an
exposure apparatus is 1.35, and the wavelength of exposure light is
193 nm. Also, the projection optical system has no aberration, and
a resist with which a substrate (wafer) is coated is not taken into
consideration. That is, as the information of the exposure
apparatus, the NA information of the projection optical system is
1.35, the .lamda. information of the exposure light is 193 nm, the
aberration information is no aberration, and no resist information
is taken into account. Also, the length of a mask pattern is
represented by the length on the image plane multiplied by the
magnification of the projection optical system. All light sources
are indicated by effective light sources on the pupil, and the
radius of the pupil is 1. Furthermore, the NA ratio of the
projection optical system to an illumination optical system will
always be 1 hereinafter. A half pitch HP (nm) of a target pattern
will be normalized by the exposure light wavelength .lamda. (nm)
and the NA, and represented by k1=HP (nm)/(.lamda.(nm)/NA).
[First Embodiment]
The first embodiment of a method of determining an effective light
source will be explained below with reference to FIGS. 3A to 3F.
FIG. 3A shows a target pattern to be formed on a substrate. Assume
that the minimum half pitch HP of the target pattern is 65 (nm).
When normalized by exposure light wavelength .lamda.=193 (nm) and
NA=1.35, the target pattern half pitch is k1=0.45. A mask was
assumed to be a halftone phase-shift mask, the transmittance of the
pattern was 100%, and that of the periphery of the pattern was 6%.
A phase difference between the pattern and the periphery of the
pattern is .pi. (rad). In the target pattern, dense holes and
isolated holes are arranged in the lateral direction. The target
pattern is not a simple periodic pattern but includes the isolated
holes, and this makes it difficult to balance the sizes of the
isolated holes and dense holes. The ordinate and abscissa of FIG.
3A showing the pattern are indicated by a length (nm) converted
into the length on the image plane. In all the drawings, the
abscissa is the X-axis, and the ordinate is the Y-axis.
FIG. 3B shows the distribution of the image function obtained by
the third image function calculation method using equation (9).
FIG. 3C shows an effective light source derived by applying this
image function and the impulse response of the projection optical
system as shown in FIGS. 2C and 2D to equation (8) (or (7)), and
suited to resolve the target pattern.
Next, a method of obtaining the image function and a method of
obtaining the effective light source will be explained below. The
image function was calculated by equation (9) by using the target
pattern itself as an approximate aerial image, and a diffracted
light distribution obtained from the target pattern. FIGS. 2C and
2D illustrate the impulse response obtained by Fourier transform of
the pupil function. When the pupil is circular and has no
aberration, a Bessel function is obtained by Fourier transform of
the pupil function. FIG. 2C shows the two-dimensional distribution
of the impulse response. FIG. 2D shows the one-dimensional section
of the impulse response. A point at which the impulse response is
zero is replaced with a nonzero finite value. In this way, the
image function distribution as shown in FIG. 3B is obtained. The
calculated image function is divided by the impulse response,
inverse Fourier transform is performed on the divided function, and
the result is divided by the complex conjugate function of the
pupil function, thereby obtaining an effective light source. Thus,
the effective light source as shown in FIG. 3C was obtained.
Then, the effective light source is obtained by deriving the image
function by the second calculation method, and compared with the
result obtained by the former third calculation method. The method
of deriving the image function by the second calculation method
will be explained in detail in the second and third embodiments, so
only the result will be explained. Pitch sampling on this image
plane is as shown in FIG. 3D. Pitch sampling is obtained from a
distribution representing the pattern periodicity, as will be
described later. The periodicity is obtained by extracting bright
peak positions from this distribution. However, in a phase-shift
mask, the periodicity may be obtained by extracting dark peak
positions, since dark peaks are notable. Referring to FIG. 3D,
.circle-solid. indicates a bright peak position, and .largecircle.
indicates a dark peak position. The periodicity is the same either
way. A circular distribution was assumed as a function representing
the shape of a pattern element.
FIG. 3E shows the calculated image function. In all of the drawings
showing pitch sampling on the image plane such as FIG. 3D and the
drawings showing the image function such as FIGS. 3B and 3E, the
ordinate and abscissa are indicated by the length (nm) on the image
plane. The computer divided the image function by the impulse
response, performed inverse Fourier transform on the divided
function, and divided the result by the complex conjugate function
of the pupil function. Then, the computer calculated the effective
light source as all negative intensities are zeros. FIG. 3F shows
the calculated effective light source. In FIGS. 3C and 3F, the
ordinate and abscissa represent coordinates on the normalized pupil
plane.
Comparison of the image functions calculated by the second and
third methods reveals that very similar distributions are obtained
by increasing the resolution of an image by increasing the number
of pixels. Accordingly, the light source distributions shown in
FIGS. 3C and 3F are very similar. When the two light source
distributions were checked by image formation simulation, the
performances were almost equal.
The effect will now be verified by image formation simulation by
using a mask pattern identical to the target pattern. An image as
shown in FIG. 4B was obtained when an image of a mask pattern (FIG.
4A) identical to the target pattern shown in FIG. 3A was formed by
illumination light obtained using the effective light source shown
in FIG. 3C or 3F as the illumination condition in the exposure
apparatus in which exposure light wavelength .lamda.=193 (nm) and
NA=1.35. The polarization distribution of the light source was
unpolarized. FIG. 4B shows the contour lines of an intensity
distribution using, as slice levels, an intensity value by which
the width of the reference pattern in the lateral direction was 65
(nm), and intensity values of .+-.10% of the former intensity
value. Consequently, it was confirmed that the contrast and shape
reproducibility were high, and the depth of focus characteristics
were also excellent although the results are omitted.
[Second Embodiment]
A method of determining an effective light source by using the same
pattern example as in the first embodiment will be explained below.
FIG. 5A shows a target pattern to be formed on a substrate. The
minimum half pitch of the target pattern is HP=50 (nm). That is,
since exposure light wavelength .lamda.=193 (nm) and NA=1.35, the
half pitch of the target pattern is k1=0.35. A mask was assumed to
be a binary mask, the transmittance of the pattern was 1, and that
of the periphery of the pattern was zero. FIGS. 5E and 5F
illustrate an image function and effective light source derived by
the second image function calculation method shown in FIG. 1B. FIG.
5E shows the image function, and FIG. 5F shows the effective light
source.
The image function deriving method using the second calculation
method will be explained in detail below. To obtain pitch sampling
from the target pattern, a computer obtained the diffracted light
distribution of the target pattern. FIG. 5B shows the diffracted
light distribution of the target pattern. More specifically, the
computer extracted diffracted light components equal to or larger
than a certain value and having the same phase, and performed
Fourier transform by including up to a region of 2NA/.lamda.,
thereby obtaining the periodicity on the image plane.
Alternatively, the periodicity may be obtained by extracting
negative in-phase diffracted light components equal to or smaller
than the certain value. The computer obtained peak positions from
the Fourier-transformed image of the diffracted light, and
extracted sampling points within a set range from these peak
positions, thereby obtaining pitch sampling on the image plane.
This pitch sampling on the image plane is as shown in FIG. 5C. The
ordinate and abscissa of FIG. 5C showing pitch sampling on the
image plane are indicated by the length (nm) on the image
plane.
Then, the computer calculated an image function. In this
embodiment, a circular distribution as shown in FIG. 5D was assumed
as a function representing the shape. FIG. 5E shows an image
function obtained by convolving this function into pitch sampling.
The computer divided the image function by the impulse response,
performed inverse Fourier transform on the divided function, and
divided the result by the complex conjugate function of the pupil
function. The computer calculated an effective light source by
regarding all negative intensities as zeros. FIG. 5F shows the
calculated effective light source. The ordinates and abscissas of
FIGS. 5C to 5E are indicated by the length (nm) on the image plane.
The ordinates and abscissas of FIGS. 5B and 5F indicate coordinates
on the normalized pupil plane.
Subsequently, a mask pattern for forming an image of the target
pattern on the image plane is formed. First, an aerial image
obtained when a pattern identical to the target pattern was used as
a mask pattern (FIG. 6B) was calculated. The illumination condition
was as shown in FIG. 6A. That is, the illumination condition was
so-called tangential polarization by which each element of the
obtained light source distribution had a polarization direction in
the tangential direction. Tangential polarization has a
polarization distribution having polarization directions in the
directions of arrows shown in FIG. 6A. An image of the mask pattern
shown in FIG. 6B was formed by the exposure apparatus in which
exposure light wavelength .lamda.=193 (nm) and NA=1.35. FIG. 6C
shows the obtained aerial image. Referring to FIG. 6C, when the
mask pattern is identical to the target pattern, the optical
proximity effect distorts the hole shape in the longitudinal
direction and makes the sizes of isolated portions and dense
portions different, thereby deteriorating the balance. To well
balance the isolated portions and dense portions, therefore, a mask
pattern is formed by correcting the proximity effect exerted on the
target pattern shown in FIG. 5A by the effective light source shown
in FIG. 5F. This method is disclosed in Japanese Patent Laid-Open
No. 2008-040470. For example, a mask pattern is formed by
calculating an approximate aerial image from the target pattern and
light source by 2D-TCC, deforming the shape of a main pattern (or
correcting the bias) based on the approximate aerial image, and
adding an auxiliary pattern. FIG. 6D shows the mask pattern thus
obtained. An image as shown in FIG. 6E was obtained when an image
of the mask pattern shown in FIG. 6D was formed under the
illumination condition as shown in FIG. 6A by using the exposure
apparatus in which exposure light wavelength .lamda.=193 (nm) and
NA=1.35. FIGS. 6C and 6E illustrate intensity contour lines using,
as slice levels, an intensity value by which the width of the
reference pattern in the lateral direction is 50 (nm), and
intensity values of .+-.10% of the former intensity value. Also,
the ordinates and abscissas of FIGS. 6B and 6D are converted into
the length (nm) on the image plane.
In the image obtained on the image plane, the isolated portions and
dense portions were well balanced, and both the shape and size were
uniform. Although no result is shown, a defocused image makes the
difference from the former image significant. The depth was large
even when compared with another illumination condition, that is,
the quadrupole illumination condition often used as the
illumination condition of holes. The light source distribution was
previously given in the method of obtaining a mask pattern from a
target pattern as disclosed in Japanese Patent Laid-Open No.
2008-040470. When adding this method of obtaining a light source as
disclosed in this patent, however, it is possible to directly
obtain a light source from a target pattern, and obtain a mask
pattern by the method disclosed in Japanese Patent Laid-Open No.
2008-040470. Accordingly, this method is regarded as a method of
generating an initial light source for obtaining a mask pattern
from a target pattern.
[Third Embodiment]
A method of determining an effective light source by using an
example of a brick wall pattern will be explained below. FIG. 7A
shows a target pattern to be formed on a substrate. The half pitch
of the target pattern in the lateral direction is HP=60 (nm). The
half pitch of the target pattern in the lateral direction is HP=60
(nm). The pattern has a width of 60 (nm) and a length of 240 (nm).
That is, since exposure light wavelength .lamda.=193 (nm) and
NA=1.35, the minimum half pitch of the target pattern is k1=0.42. A
mask was assumed to be a binary mask, the transmittance of the
pattern was 1, and that of the periphery of the pattern was
zero.
In process 1, an image function was obtained by the second
calculation method shown in FIG. 1B. In process 14 of FIG. 1B, as
the function representing the shape of an element forming the
target pattern, a function when the element shape was assumed to be
an elliptic shape and a function when the element shape was assumed
to be a circular shape were compared. After the image function was
calculated, processes 2 to 4 shown in FIG. 1A were performed to
obtain effective light sources. FIG. 7B shows an effective light
source when the pattern element was assumed to have an elliptic
shape. FIG. 7C shows an effective light source when the pattern
element was assumed to have a circular shape.
The way an image of the target pattern was formed by each of these
light sources was checked. An image of a mask pattern identical to
the target pattern shown in FIG. 7A was formed by an exposure
apparatus using each of the effective light sources shown in FIGS.
7B and 7C as an illumination condition. The polarization
distribution of the illumination condition was so-called tangential
polarization by which each element of the obtained effective light
source had a polarization direction in the tangential direction.
FIGS. 7D and 7E respectively illustrate two-dimensional images
obtained from the effective light sources shown in FIGS. 7B and 7C.
FIGS. 7D and 7E illustrate intensity contour lines using, as slice
levels, an intensity value by which the width of the reference
pattern in the lateral direction is 60 (nm), and intensity values
of .+-.10% of the former intensity value. The intensity
distribution (FIG. 7D) obtained from the effective light source
shown in FIG. 7B was superior in contrast and shape
reproducibility, and also superior in focus characteristics
although the results will be omitted. This indicates that when
calculating an image function by the second calculation method
shown in FIG. 1B, it is important to set a function expressing the
shape of a target pattern so that the image function has a proper
distribution.
[Fourth Embodiment]
A projection optical system only considers a defocus aberration,
and does not consider a resist with which a substrate (wafer) is
coated. Let def(unit:nm) be the defocus amount of an image plane.
In this case, letting .PHI. be an aberration function, by
considering an aberration in a pupil function P(f,g) in equation
(7) or (8), equation (10) below can be obtained.
P(f,g)=exp[-2.pi.i/.lamda..PHI.(f,g)] (10)
For example, only considering defocus as an aberration, the
aberration function .PHI. is expressed by: .PHI.(f,g)=defn(1-
{square root over (1-(NA/n).sup.2(f.sup.2+g.sup.2))}{square root
over (1-(NA/n).sup.2(f.sup.2+g.sup.2))} (11) where n represents the
refractive index of a medium.
When expanded by Zernike coefficients, the aberration function
.PHI. can be expressed as follows. Assume that the coordinates of a
pupil are polar coordinates (.rho.,.theta.)
(0.ltoreq..rho..ltoreq.1 and 0.ltoreq..theta..ltoreq.2.pi.).
.PHI..function..rho..theta..infin..times..times..times..times..times..fun-
ction..rho..infin..times..times..times..times..function..rho..times..times-
..times..times..times..theta. ##EQU00004## where n and m are
integers, and meets n.gtoreq.m.gtoreq.1, A.sub.nm is a coefficient,
and R.sub.n.sup.m(.rho.)cos m.theta. is an orthogonal function
system.
In this embodiment, an effective light source is determined by
using equations (10) and (11). FIG. 9A shows a target pattern to be
formed on the substrate. Assume that the minimum half pitch HP of
the target pattern is 65 (nm). When normalized by exposure light
wavelength .lamda.=193 (nm) and NA=1.35, the target pattern half
pitch is k1=0.45. A mask was assumed to be a halftone phase-shift
mask, the transmittance of the pattern was 100%, and that of the
periphery of the pattern was 6%. A phase difference between the
pattern and the periphery of the pattern is .pi. (rad). The
ordinate and abscissa of FIG. 9A showing the pattern are indicated
by a length (nm) converted into the length on the image plane. In
all the drawings, the abscissa is the X-axis, and the ordinate is
the Y-axis.
A light source distribution is calculated from the target pattern
by considering a defocus aberration. Any of the above-described
three calculation methods may be used as an image function
calculation method. When using the third calculation method, an
approximate aerial image I(x,y) in equation (9) needs to be
different from that in a case including no aberration. Assume,
however, that they are equal. That is, an image function is
obtained by assuming that the approximate aerial image I(x,y) is
equal to the target pattern itself or a partial image of the target
pattern.
A light source distribution is calculated from the obtained image
function by using equation (7) or (8). In this step, an impulse
response is obtained by performing Fourier transform on the pupil
function of equation (10), and a response length is obtained based
on the length to the second zero point of the impulse response. The
response length in a case including an aberration is different from
that in a case including no aberration.
A case considering a defocus aberration is compared with that not
considering a defocus aberration. In this case, def=50 (nm) is set
as a defocus amount. As a defocus amount, 50 to 70% of a required
depth, that is, 0.5 to 0.7.lamda./NA.sup.2 is set. Alternatively,
an aberration is set so that the central intensity of the impulse
response does not become lower than the peripheral intensity. The
response length to the second zero point of the impulse response
when there is such aberration may be substituted for that when
there is no aberration.
FIG. 9B shows a light source distribution calculated from equation
(7) (or (8)) by assuming that there is no aberration, that is,
.PHI.=0 in equation (10). FIG. 9C shows a mask pattern obtained
from the light source distribution. FIG. 9D shows a light source
distribution calculated from equation (7) (or (8)) by considering a
defocus aberration, that is, by assuming def=50 (nm) in equation
(11). FIG. 9E shows a mask pattern obtained from the light source
distribution. By considering a defocus aberration, a light source
distribution and mask pattern different from those in a case not
considering a defocus aberration are obtained.
The performances are verified by image formation simulation using
those light source distributions and mask patterns. In the image
formation simulation, an exposure apparatus, in which exposure
light wavelength .lamda.=193 (nm) and NA=1.35, forms an image of
the mask pattern shown in FIG. 9C or 9E by illumination light
obtained using the effective light source shown in FIG. 9B or 9D as
the illumination condition. The image formation simulation was done
by changing the defocus amount.
Performance assessment is done by obtaining a change amount in line
width (CD) of a two-dimensional image when changing the defocus
amount. A value such that the width of a reference pattern in the X
direction becomes 65 (nm) is obtained as a reference slice level
from an aerial image obtained at the best focus. Then, an aerial
image is obtained as a two-dimensional image for each defocus
amount by using the contour lines of the reference slice level,
thereby obtaining the line width (CD) of the two-dimensional image.
In this way, the CD for the defocus amount is obtained, and the
image formation performances of the light source considering an
aberration and that not considering an aberration are compared.
FIG. 10 shows the result. Referring to FIG. 10, black lines
indicate the CD obtained from the aerial image obtained from the
mask and the light source considering a defocus aberration, and
gray lines indicate the CD obtained from the aerial image obtained
from the mask and the light source not considering a defocus
aberration. As shown in FIG. 10, the light source considering an
aberration is less sensitive to a change in focus, that is,
superior in focus characteristics. Although the results will be
omitted, it has been ensured that the light source considering an
aberration is superior in focus characteristics even when using the
same mask pattern. This, therefore, means that the light source
distribution considering an aberration reduces a decrease in image
formation performance due to an aberration. Furthermore, although
the light source distribution considering a defocus aberration is
shown in this embodiment, it is possible to calculate a light
source distribution using an arbitrary aberration function by using
equation (12).
[Exposure Apparatus]
An exposure apparatus 100 that illuminates an original with light
emitted from an illumination optical system and exposes a substrate
by projecting a pattern of the illuminated original onto the
substrate via a projection optical system will be explained below
with reference to FIG. 8. FIG. 8 is a schematic block diagram
showing the arrangement of the exposure apparatus 100. In the
exposure apparatus 100, an illumination optical system 180 forms an
effective light source corresponding to effective light source data
generated by executing the generation program described previously.
The exposure apparatus 100 illuminates a mask 120 formed based on
the light source data generated by executing the above-described
generation program. In this embodiment, the exposure apparatus 100
is a projection exposure apparatus that exposes a wafer 140 to the
pattern of the mask 120 by the step-and-scan method. However, the
exposure apparatus 100 is also applicable to the step-and-repeat
method or another exposure method. As shown in FIG. 8, the exposure
apparatus 100 includes an illuminating device 110, a reticle stage
(not shown) for supporting the mask 120, a projection optical
system 130, and a wafer stage (not shown) for supporting the wafer
140. The illuminating device 110 illuminates the mask 120 having a
circuit pattern to be transferred, and includes a light source 160
and the illumination optical system 180. The light source 160 is an
excimer laser such as an ArF excimer laser having a wavelength of
about 193 nm, or a KrF excimer laser having a wavelength of about
248 nm. However, the light source 160 is not limited to the excimer
laser, and can also be an F2 laser having a wavelength of about 157
nm, a narrow-band mercury lamp, or the like.
The illumination optical system 180 is an optical system for
illuminating the mask 120 by using light from the light source 160.
In this embodiment, the illumination optical system 180 illuminates
the mask 120 by forming an effective light source corresponding to
the effective light source data generated by executing the
above-described generation program. The illumination optical system
180 includes a relay optical system 181, an optical system 182 for
shaping a beam, a polarization controller 183, a phase controller
184, an optical element 185 for saving the exit angle, a relay
optical system 186, and a multi-beam generator 187. The
illumination optical system 180 also includes a polarization state
adjusting unit 188, computer hologram 189, relay optical system
190, aperture 191, zoom optical system 192, multi-beam generator
193, aperture stop 194, and irradiation unit 195. The relay optical
system 181 deflects the light from the light source 160, and guides
the deflected light to the optical system 182 for shaping a beam.
The optical system 182 for shaping a beam converts the aspect ratio
of the dimensions of the sectional shape of the light from the
light source 160 into a desired value (for example, changes the
sectional shape from a rectangle to a square), thereby shaping the
sectional shape of the light from the light source 160 into a
desired shape. The optical system 182 for shaping a beam forms a
light beam having a size and divergence angle required to
illuminate the multi-beam generator 187.
The polarization controller 183 includes a linear polarizer or the
like, and has a function of removing unnecessary polarization
components. By minimizing polarization components to be removed
(shielded) by the polarization controller 183, the light from the
light source 160 can efficiently be converted into desired linearly
polarized light. The phase controller 184 converts the linearly
polarized light obtained by the polarization controller 183 into
circularly polarized light by giving a phase difference of
.lamda./4 to the linearly polarized light. The optical element 185
for saving the exit angle includes, for example, an optical
integrator (a fly-eye lens made up of a plurality of microlenses, a
fiber bundle, or the like), and outputs light at a predetermined
divergence angle. The relay optical system 186 concentrates the
exit light from the optical element 185 for saving the exit angle
to the multi-beam generator 187. The relay optical system 186 gives
the Fourier transform relationship (the relationship between an
object plane and pupil plane or between the pupil plane and an
image plane) to the exit surface of the optical element 185 for
saving the exit angle and the incident surface of the multi-beam
generator 187. The multi-beam generator 187 includes an optical
integrator (a fly-eye lens made up of a plurality of microlenses, a
fiber bundle, or the like) for uniformly illuminating the
polarization state adjusting unit 188 and computer hologram 189.
The exit surface of the multi-beam generator 187 forms a light
source surface made up of a plurality of point light sources. The
existing light from the multi-beam generator 187 enters, as
circularly polarized light, the polarization state adjusting unit
188.
The polarization state adjusting unit 188 converts the circularly
polarized light obtained by the phase controller 184 into linearly
polarized light having a desired polarization direction by giving a
phase difference of .lamda./4 to the circularly polarized light.
The exit light from the polarization state adjusting unit 188
enters, as linearly polarized light, the computer hologram 189 as a
diffraction optical element. The polarization state adjusting unit
188 is placed closer to the light source side than the computer
hologram 189, but may be placed on the opposite side. It is also
possible to form the polarization state adjusting unit as an SWS
(Sub Wavelength Structure), and integrate the SWS with the
diffraction optical element. That is, one element can be formed to
have the functions of both the polarization state adjusting unit
and diffraction optical element. When circularly polarized light
enters, light having passed through the polarization state
adjusting unit 188 is converted into linearly polarized light
having a desired polarization direction, and this linearly
polarized light enters a predetermined portion of the computer
hologram 189, thereby forming an arbitrary light source
distribution having an arbitrary polarization direction (see FIG.
5B).
The computer hologram 189 forms a desired light intensity
distribution such as an effective light source having tangential
polarization, at the position of the aperture 191 via the relay
optical system 190. The computer hologram 189 can also form annular
illumination, quadrupole illumination, and the like, and can
achieve a desired polarization distribution such as tangential
polarization or radial polarization together with the polarization
state adjusting unit 188. A plurality of computer holograms 189 for
forming different effective light sources are arranged in a
switching unit such as a turret. The polarization state adjusting
unit 188 is also changeable. Various kinds of effective light
sources can be implemented by arranging, in the optical path of the
illumination optical system 180, the computer holograms 189
corresponding to the effective light source data generated by a
processing apparatus described above.
The aperture 191 has a function of passing only the light intensity
distribution formed by the computer hologram 189. The computer
hologram 189 and aperture 191 are arranged to have the relationship
of the Fourier transform plane. The zoom optical system 192
enlarges the light intensity distribution formed by the computer
hologram 189 by a predetermined magnification, and projects the
enlarged distribution onto the multi-beam generator 193. The
multi-beam generator 193 is placed on the pupil plane of the
illumination optical system 180, and forms, on the exit surface, a
light source image (effective light source distribution)
corresponding to the light intensity distribution formed at the
position of the aperture 191. In this embodiment, the multi-beam
generator 193 is an optical integrator such as a fly-eye lens or
cylindrical lens array. Note that the aperture stop 194 is formed
near the exit surface of the multi-beam generator 193. The
irradiation unit 195 includes a condenser optical system, and
illuminates the mask 120 with the effective light source
distribution formed on the exit surface of the multi-beam generator
193.
The mask 120 is formed based on mask data generated by the
processing apparatus described previously, and has a circuit
pattern (main pattern) to be transferred and an auxiliary pattern.
The mask 120 is supported and driven by the mask stage (not shown).
Diffracted light emitted from the mask 120 is projected onto the
wafer 140 via the projection optical system 130. Since the exposure
apparatus 100 is a step-and-scan type exposure apparatus, the
pattern of the mask 120 is transferred onto the wafer 140 by
scanning the mask 120 and wafer 140. The projection optical system
130 is an optical system for projecting the pattern of the mask 120
onto the wafer 140. A refracting system, cata-dioptric system, or
reflecting system can be used as the projection optical system 130.
The wafer 140 is a substrate onto which the pattern of the mask 120
is to be projected (transferred), and is supported and driven by
the wafer stage (not shown). However, it is also possible to use a
glass plate or another substrate instead of the wafer 140. The
wafer 140 is coated with a photoresist. During exposure, the
illumination optical system 180 illuminates the mask 120 with the
light emitted from the light source 160. The projection optical
system 130 forms, on the wafer 140, an image of the light
reflecting the pattern of the mask 120. In this step, the mask 120
formed based on the mask data generated by the above-described
processing apparatus is illuminated with the effective light source
corresponding to the effective light source data generated by the
processing apparatus.
Accordingly, the exposure apparatus 100 can economically provide
high-quality devices (for example, a semiconductor element, an LCD
element, an image sensing element (such as a CCD), and a thin-film
magnetic head) with a high throughput by multiple exposure.
[Device Manufacturing Method]
A method of manufacturing a device (for example, a semiconductor
device or liquid crystal display device) of an embodiment of the
present invention will be explained below. A semiconductor device
manufacturing method will be explained as an example. A
semiconductor device is manufactured through a pre-process of
forming an integrated circuit on a wafer, and a post-process of
completing, as a product, the integrated circuit chip on the wafer
formed in the pre-process. The pre-process includes a step of
exposing a wafer coated with a photosensitive agent by using the
above-described exposure apparatus, and a step of developing the
wafer. The post-step includes assembling steps (dicing and
bonding), and a packaging step (encapsulation). Note that a liquid
crystal display device is manufactured through a step of forming a
transparent electrode. The step of forming a transparent electrode
includes a step of applying a photosensitive agent onto a glass
substrate on which a transparent conductive film is deposited, a
step of exposing the glass substrate coated with the photosensitive
agent by using the above-described exposure apparatus, and a step
of developing the glass substrate. The device manufacturing method
of this embodiment can manufacture a device superior in quality to
the conventional devices.
[Other Embodiments]
Aspects of the present invention can also be realized by a computer
of a system or apparatus (or devices such as a CPU or MPU) that
reads out and executes a program recorded on a memory device to
perform the functions of the above-described embodiment(s), and by
a method, the steps of which are performed by a computer of a
system or apparatus by, for example, reading out and executing a
program recorded on a memory device to perform the functions of the
above-described embodiment(s). For this purpose, the program is
provided to the computer for example via a network or from a
recording medium of various types serving as the memory device (for
example, computer-readable medium). In such a case, the system or
apparatus, and the recording medium where the program is stored,
are included as being within the scope of the present
invention.
While the present invention has been described with reference to
exemplary embodiments, it is to be understood that the invention is
not limited to the disclosed exemplary embodiments. The scope of
the following claims is to be accorded the broadest interpretation
so as to encompass all such modifications and equivalent structures
and functions.
This application claims the benefit of Japanese Patent Application
No. 2009-265530, filed Nov. 20, 2009 and No. 2010-240106, filed
Oct. 26, 2010, which are hereby incorporated by reference herein in
their entirety.
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